Actually, I do find it moderately useful. By checking the backlinks section of Google Webmaster Tools, I can get a rough idea of which topics within my site are attracting the most interest and discussion. That it turn helps me to decide which areas to further develop and optimise.

I also find it useful to check the broken links section in GWM - those that trigger a 404 error on my site. These are incoming links where the domain is correct but other parts of the URL are in error. It can sometimes be useful to contact the sites from which these link comes, and ask them to fix the errors.

I'm not saying these are high priority actions or that they'll prove worthwhile for everyone. But I wouldn't dimiss them either.

Actually, I do find it moderately useful. By checking the backlinks section of Google Webmaster Tools, I can get a rough idea of which topics within my site are attracting the most interest and discussion. That it turn helps me to decide which areas to further develop and optimise.

I also find it useful to check the broken links section in GWM - those that trigger a 404 error on my site. These are incoming links where the domain is correct but other parts of the URL are in error. It can sometimes be useful to contact the sites from which these link comes, and ask them to fix the errors.

I'm not saying these are high priority actions or that they'll prove worthwhile for everyone. But I wouldn't dimiss them either.

I don't normally advise people to invest a lot of time in researching their backlinks, but you have given two very good reason. Here are some more reasons to check your backlinks once in a while.

Scrapers sometimes link back to you -- I sometimes leave the scraper sites alone. If I outrank them, and they give proper attribution, and their links don't use "rel='nofollow'", and their sites are not infested with malware, I may be inclined to let them be simply because there are so many of them. But I want to know who is scraping my content and whether they are being so stingy as to not even give me a decent link. I just went through an exchange with an ISP over a cheap scraper site last night where the idiot nofollowed the link. His site is gone, now.

Growth in organic backlinks -- For an established site, if you don't have a healthy trendline in referral traffic then you're doing something wrong. Even ecommerce sites get such links from time to time because people recommend products, merchants, use product pages to illustrate points about items, etc. If I see a dropoff in backlink growth then I suspect something is wrong (or else the site has cut back on publishing new content).

Identifying new influencers -- Every now and then someone comes along who builds a successful community that is relevant to your site. And when they notice you, they can send you tons of traffic. It may be worthwhile building a relationship with that community (by participating in it and supporting it).

I can get a rough idea of which topics within my site are attracting the most interest and discussion. That it turn helps me to decide which areas to further develop and optimise.

Your site logs or traffic analyser will give you FAR better insight into what topics are popular than link counting will, and looking at the links that send visitors will tell where, what and how your promotional stategies and your optimising efforts should be focussed.